|
%I #9 Sep 13 2018 02:56:57
%S 6,2,2,7,2,7,0,9,4,3,1,3,6,9,5,1,0,3,7,9,5,0,3,9,9,3,9,2,8,6,5,2,2,8,
%T 9,0,1,3,8,6,1,8,3,1,8,7,7,3,8,7,6,7,8,7,6,6,7,6,5,5,3,8,3,7,6,3,8,3,
%U 2,5,8,1,7,2,4,1,3,6,6,9,8,0,6,9,0,3,0,9,2,9,6,2,6,6,8,6,3,8,4
%N Decimal expansion of least x satisfying 7*x^2 - 1 = csc(x) and 0<x<Pi.
%C See A201564 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A201674/b201674.txt">Table of n, a(n) for n = 0..10000</a>
%e least: 0.62272709431369510379503993928652289013...
%e greatest: 3.12676335481784395832471054304139350...
%t a = 7; c = -1;
%t f[x_] := a*x^2 + c; g[x_] := Csc[x]
%t Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201674 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
%t RealDigits[r] (* A201675 *)
%o (PARI) a=7; c=-1; solve(x=0.5, 1, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Sep 12 2018
%Y Cf. A201564.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 04 2011
|
